His first professional season was 1978. He split the season between the Daytona Beach Astros and Columbus Astros. He went 1–2 with a 1.20 ERA in three games with Daytona Beach and 5–5 with a 4.18 ERA in 11 games with Columbus. In 1979, Boxberger played with the Columbus Astros again, going 6–7 with a 4.80 ERA in 21 games. For the third year in a row, Boxberger played with Columbus again in 1980, and for the third year in a row his stats dropped. He went 4–13 with a 5.62 ERA in 23 games in 1980.
He wound up in the New York Yankees organization in 1981, playing for the Double-A Nashville Sounds. He went 4–9 with a 4.54 ERA in 23 games that year. Boxberger played the final two years of his professional career in the California Angels organization. In 1982, he played for the Holyoke Millers, going 5–9 with a 3.78 ERA. He played for the Nashua Angels in 1983, going 5–10 with a 5.43 ERA.